Here is an essay by Brett Hall about what the philosophy of science is and what it tries to achieve. It makes several claims that I think would be great starting points for building any future syllabus for science education. Chief among them is the idea that science's mission "is not to 'support' theories with evidence.... The truth is that science is about correcting errors in our explanations." (Emphasis by the original author.)
Hall's point, a restatement of Sir Karl Popper's chief insight, is that science is necessarily tentative and incremental. We always have to be ready to accept the possibility that what we know is incomplete. But if we have a theory that is invalidated by new evidence, it doesn't always mean the whole of the original theory is wrong; it just didn't cover the full range of cases that we are familiar with. (See: Newton's physics vs. Einstein's physics.)
Or it might mean that the new evidence is in fact bogus, or itself incomplete, or misunderstood, etc. You cannot use this as an excuse to junk existing understandings wholesale in the light of a single anomalous result:
Under the prevailing view of how science works - if an experiment critically wounds a theory such that it is once-and-for-all falsified and so liable to be rejected - then what can we jump to? If we reject our best theory and there is no rival - the process of rejection does not provide any new explanation for us. The negation of a theory is not a new theory.
Emphasis mine (this time).
As of late there's been much talk about low-quality science — poor reproduction rates for results from widely ballyhooed studies and the like. Some twits have been using this as a wedge argument to attack science per se by way of the old "other ways of knowing" ploy, but the answer to badly practiced science is not no science at all; it's to remove the perverse incentives that make it hard to practice science in a way that allows for the progressive correction of error in our understanding of things.